Trying to calculate the square root of a positive number based on the “divide and average” scheme.

I am re-posting this as it would not post correctly earlier.

I am trying to calculate the square root of a positive number, a, based on the “divide and average” scheme. The scheme is formulated in the following:

x = ( x + a/x) / 2

My function, however, returns incorrect results. I was hoping someone could help me debug it.

function v = my_sqrtD(t)

%find the square root of t, and t must be larger than 0.

v_pre = t/2.0;

my_eps = 0.0001;

%when the limit is reached, stop the loop

n_limit = 1000000;

for i=1:n_limit

   v = (v_pre + t/v_pre)/2.0;

   res = abs((v-v_pre)/v);

   if res < my_eps, break, end

end %end of loop

if (i==n_limit)

   disp('The root cannot be found.');

end

Answer 1

[Roger Stafford]

The line

v = (v_pre + t/v_pre)/2.0;

is your trouble. It should read:

v_pre = (v_pre + t/v_pre)/2.0;

However, you will have to appropriately revise your computation of 'res'.

[NikePro]

How would i go about revising it?

[Roger Stafford]

I've changed it a bit:

   for i=1:n_limit
     v = (v_pre + t/v_pre)/2.0;
     res = abs((v-v_pre)/v);
     v_pre = v;  % <-- Update v_pre (That's what was missing)
     if res < my_eps, break, end
     ...